Pure and Applied Mathematics Journal
Volume 3, Issue 6-2, December 2014, Pages: 1-5
Received: Oct. 8, 2014;
Accepted: Oct. 11, 2014;
Published: Oct. 24, 2014
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Francisco Bulnes, Head of Research Department, Research Department in Mathematics and Engineering, TESCHA, Federal Highway, Mexico-Cuautla Tlapala “La Candelaria”, Chalco, P. C. 56641, Mexico
The integral geometry methods are applied on deformed categories to obtain correspondences in the geometrical Langlands program and construct the due equivalences between geometrical objects of the moduli stacks and algebraic objects of the corresponding categories and their L_(G-opers) characterizing the solution classes to field theory equations in the belonging cohomological context such as H^0 (g[[z] ],V_critical )=C[Op_LG (D^X)] which is natural in the framework of the integral transforms to the generalizing of the Zuckerman functors that will be useful to the obtaining of the different factors of the universal functor of derived sheaves of Harish-Chandra to the Langlands geometrical program in mirror symmetry. The cosmological problem that exists is to reduce the number of field equations that are resoluble under the same gauge field (Verma modules) and to extend the gauge solutions to other fields using the topological groups symmetries that define their interactions. This extension can be given by a global Langlands correspondence between the Hecke sheaves category H_(G^^ ) ∞ on an adequate moduli stack and the holomorphic L_(G-) bundles category with a special connection (Deligne connection). The corresponding 〖D 〗_-modules may be viewed as sheaves of conformal blocks (or co-invariants) (images under a generalized version of the Penrose transform) naturally arising in the framework of conformal field theory.
Integral Geometry Methods on Deformed Categories in Field Theory II, Pure and Applied Mathematics Journal. Special Issue: Integral Geometry Methods on Derived Categories in the Geometrical Langlands Program.
Vol. 3, No. 6-2,
2014, pp. 1-5.
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